where E'(x)=E(x)/1-v(x) In Eqs. (4),(5), E(r) and v(x)are the elastic modulus and Poisson ratio distributions along x-axis, respectively. Value of E(x) is the strain non-associated with stress. It is associated with thermal expansion or/and with a volume change due to a crystallographic phase transformation. The static balance conditions [12] in the chosen coordinate system result in a system of linear equations with Inknown values Eo and k Fa+bo(x, Eo, k )dk=0, ,k) here Fa is the applied axial force and Ma is the applied bending moment. Solution of the system is [13] I2Jo-Fa/ b)+I01-Malb Eo 1012 11Jo-Fa/b)-lo(1-Ma/b) k whe L=rE'(x)dx (=0, 1, 2), (8) 0,1) Note that the superposition principle is valid for this problem. It permits to express the stress variation along rack path in a specimen as 0(x)=0a(x)+G(x), (10) where ga(x) is the bending stress in the prospective crack path in the absence of any residual stresses, and o(r)is the macroscopic residual stress distribution In [3], the bending stress oa(x) was expressed as follows 0a(x)=0m where om is the applied stress on tensile surface of bending specimen. It is well known that 15Ps 6M Here P is the critical load(applied bending load corresponding to the specimen failure)and s is the support span lowever, the differences in the elastic moduli of the layers were not taken into account in [ 3]. Difference in elasticwhere E x Ex x ′( ) ( ) [ ( )]. = −1 ν (5) In Eqs. (4), (5), E x( ) and ν( ) x are the elastic modulus and Poisson ratio distributions along x-axis, respectively. Value of ~ε ( ) x is the strain non-associated with stress. It is associated with thermal expansion or/and with a volume change due to a crystallographic phase transformation. The static balance conditions [12] in the chosen coordinate system result in a system of linear equations with unknown values ε 0 and k: F b x k dk M bx x k dx a w a w + = + = ⎧ ⎨ ⎪ ⎪ ⎩ ⎪ ⎪ ∫ ∫ σ ε σ ε (, , ) , (, , ) , 0 0 0 0 0 0 (6) where Fa is the applied axial force and Ma is the applied bending moment. Solution of the system is [13]: ε 0 2 0 11 1 2 0 2 = − +− − I J Fb IJ M b I II a a ( )( ) , (7a) k IJ Fb I J M b I II a a = −−− − 10 01 1 2 0 2 ( )( ) , (7b) where I x E x dx j j j w = ′ = ∫ ( ) ( , , ), 012 0 (8) J x x E x dx j j j w = ′ = ∫ 0 0 1 ~ε ( ) ( ) ( , ). (9) Note that the superposition principle is valid for this problem. It permits to express the stress variation along the crack path in a specimen as σσ σ ( ) ( ) ( ), xxx = + a r (10) where σa ( ) x is the bending stress in the prospective crack path in the absence of any residual stresses, and σr ( ) x is the macroscopic residual stress distribution. In [3], the bending stress σa ( ) x was expressed as follows: σ σ a m x x w () , = − ⎛ ⎝ ⎜ ⎞ ⎠ 1 ⎟ 2 (11) where σ m is the applied stress on tensile surface of bending specimen. It is well known that σ m Ps a bw M bw = = 1 5 6 2 2 . . (12) Here P is the critical load (applied bending load corresponding to the specimen failure) and s is the support span. However, the differences in the elastic moduli of the layers were not taken into account in [3]. Difference in elastic 294